Modelling the saturation major loop of a ferrous metal produces the intrinsic magnetization parameters; fitting the measured commutation curve, however, can yield different results. The relation of the intrinsic loci of the vertices of the minor loops ( ) to the experimental curve ( ) is investigated. The two-way transformation between the two curves is formulated in closed mathematical form with the help of the internal demagnetization factor, . The method is applied to four ferrous metals, with widely different intrinsic properties (soft nonoriented Fe-Si steel, normalized low carbon steel, and Finemet in nanocrystalline and amorphous state) supporting the predictions of the proposal. The developed relationship is model independent and it is shown that the factor depends linearly on coercivity based on experimental evidence. 1. Introduction A large number of the measurements of ferrous substances are aimed at finding the intrinsic material properties [1] of the tested ferrous sample (as defined by Fiorillo). Due to the ever-presence of demagnetization field, various measuring methods have been developed to minimize its effect. The most commonly accepted way is to make the sample turn into a closed magnetic circuit, such as a toroid or an Epstein square [1–3]. Although these two methods are not completely free from the ever-present internal demagnetization, they suffer the least from it [1]. Researchers went into great length to include the internal demagnetization force into current models like Preisach, Jiles, Stoner-Wohlfarth [2, 4, 5], and so forth, leading to complicated, so called, dynamic versions. The saturated major hysteresis loop of the sample carries all the intrinsic magnetic parameters directly recoverable from the measured data. Within this loop lie the un-hysteretic loci of the vertices of the symmetrical minor loops, the only curve, which belongs to both the ascending and descending branches of the hysteresis loops [5, 6]. A proposal is put forward in this paper to show the relationship between the intrinsic curve and the loci of vertices of the measured minor loops. This relationship between the two curves, independent of models, is formulated in closed mathematical form and its prediction is verified by the experimental data obtained from four different ferrous samples. Once the intrinsic locus ( for ) is modelled from saturation or minor loop data, by using any of the static models, the measured curve ( ) can be calculated from the proposed formulation below with optimization of the parameter value as specified by Jiles [2] and used
References
[1]
F. Fiorillo, Measurement and Characterization of Magnetic Materials, Elsevier, Oxford, UK, 2004.
[2]
D. Jiles, Introduction to Magnetism and Magnetic Materials, Chapman and Hall, New York, NY, USA, 1998.
[3]
T. Nakata, N. Takahashi, K. Fujiwara, M. Nakano, Y. Ogura, and K. Matsubara, “An improved method for determining the DC magnetization curve using a ring specimen,” IEEE Transactions on Magnetics, vol. 28, no. 5, pp. 2456–2458, 1992.
[4]
F. Preisach, “Uber die magnetische Nachwirkung,” Zeitschrift für Physik, vol. 94, pp. 227–302, 1935.
[5]
E. C. Stoner and E. P. Wohlfarth, “A mechanism of magnetic hysteresis in heterogeneous alloys,” IEEE Transactions on Magnetics, vol. 27, no. 4, pp. 3475–3518, 1991.
[6]
J. Takacs, “The everett integral and its analytical approximation,” in Advanced Magnetic Materials, L. Malkinsk, Ed., pp. 203–230, Intech, 2012.
[7]
J. Takacs, “A phenomenological mathematical model of hysteresis,” Compel, vol. 20, no. 4, pp. 1002–1014, 2001.
[8]
I. Meszaros, Private communication on m0.
[9]
H. Hauser, Y. Melikhov, and D. C. Jiles, “Examination of the equivalence of ferromagnetic hysteresis models describing the dependence of magnetization on magnetic field and stress,” IEEE Transactions on Magnetics, vol. 45, no. 4, pp. 1940–1949, 2009.
[10]
G. Bertotti, Hysteresis in Magnetism, Academic Press, San Diego, Calif, USA, 1998.
[11]
D. C. Jiles and D. L. Atherton, “Theory of ferromagnetic hysteresis,” Journal of Magnetism and Magnetic Materials, vol. 61, no. 1-2, pp. 48–60, 1986.
[12]
J. A. Brug and W. P. Wolf, “Demagnetizing fields in magnetic measurements. I. Thin discs,” Journal of Applied Physics, vol. 57, no. 10, pp. 4685–4694, 1985.
[13]
A. Benabou, J. V. Leite, S. Clénet, C. Sim？o, and N. Sadowski, “Minor loops modelling with a modified Jiles-Atherton model and comparison with the Preisach model,” JMMM, vol. 320, no. 20, pp. e1034–e1038, 2008.
[14]
R. G. Harrison, “Physical theory of ferromagnetic first-order return curves,” IEEE Transactions on Magnetics, vol. 45, no. 4, pp. 1922–1939, 2009.
[15]
L. K. Varga, Gy. Kovacs, and J. Takacs, “Anhysteretic and biased first magnetization curves for Finemet-type toroidal samples,” JMMM, vol. 320, no. 3-4, pp. L.26–L.29, 2008.
[16]
J. Takacs, “Barkhausen instability and its implication in T(x) modelling of hysteresis,” Compel, vol. 24, no. 4, pp. 1180–1190, 2005.
[17]
J. Takacs, Mathematics of Hysteretic Phenomena, Wiley, Berlin, Germany, 2003.
